Few women and even fewer African Americans, Latinos, and Native Americans complete doctoral degrees in mathematics in the United States. This article proposes a framework for understanding the small numbers of women and students of color who persist in doctoral mathematics based on the notion that academic and social integration are critical to persistence and that integration develops through particular types of participation in the communities of practice of graduate school. An integrated summary of previous research on attrition and persistence of doctoral students identifies particular obstacles faced by women and students of color in doctoral mathematics and directs attention to ways in which faculty and others involved in doctoral education can work to improve the persistence rates, experiences, and diversity of their doctoral students. (Contains 2 figures, 2 tables, and 7 notes.)